Fundamental Approach to TRIGA Steady-State Thermal-Hydraulic CHF Analysis

National Organization of Test, Research, and Training Reactors (TRTR) Meeting

Lincoln City, OregonSeptember 17-20, 2007

Earl E. Feldman

2

Outline

Two-Step Process (Step 1: Flow; Step 2: CHF)

Flow

– Coolant channel geometry of models

– Computer codes (STAT & RELAP5)

– Nodal structure of RELAP5 models used to determine flow

– List representative parameters for two generic TRIGA reactors -- a hexagonal pitch TRIGA and a rectangular pitch TRIGA

– Compare STAT and RELAP5 flow results for a representative hexagonal pitch TRIGA reactor

3

Outline (continued)

Critical Heat Flux (CHF)

– Bernath correlation

– Groeneveld tables (1986, 1995, 2006)

– Hall and Mudawar (Purdue) outlet correlation

– PG-CHF (Czech Republic) correlations

– Compare CHF correlations for representative TRIGA reactor conditions

– Compare CHF power predictions for a representative hexagonal pitch TRIGA reactor

Suggested Approach to CHF

Conclusions

4

Geometric Model for Calculation of Coolant Flow Rates (Step 1)

The core flow area is divided into subchannels defined by the cusps between adjacent fuel rods.

Assume no mass exchange or heat transfer between adjacent subchannels, i.e, each subchannel behaves independently of its neighbors and can be analyzed separately.

Only potentially limiting subchannels need be considered.

Divide the length of the subchannel being analyzed into a series of horizontal layers or nodes. The 15-inch (0.381-m) heated length was divided into 15 1-inch layers.

Subchannel

Fuel Rod

Fuel Rod Fuel Rod

Fuel Rod

5

Codes Being Used for Thermal-Hydraulic Analysis

STAT

– GA-developed code with fixed geometry of one subchannel.

– Custom made for TRIGA reactor hydraulics.

– Steady state only.

– No fuel rod temperature model

– Has 2 CHF correlations• Bernath (1960)• McAdams (1949)

RELAP5-3D (Version 2.3)

– Current developer is the Idaho National Laboratory

– General transient thermal-hydraulic neutronics reactor code. No fixed geometry. Uses a series of coolant nodes and junctions. Heat structures attached to coolant nodes represent solid regions, such as fuel rods.

– Has 2 CHF correlation options• 1986 Groeneveld table• PG-CHF from the Czech Republic (~1994)

6

RELAP5 Thermal-Hydraulic Model for Current Analysis

Source Sink

ColdLeg

LowerReflectorCoolant(1 node)

HorizontalConnector

Fuel RodCoolant

(15 nodes)

UpperReflectorCoolant

(2 nodes)

ChimneyCoolant(1 node)

UpperReflector

FuelRod

LowerReflector

7

Representative TRIGA Generic Reactor Parameters(Not the Most Limiting Values for Safety Analysis)

Reactor

Parameter Hexagonal Pitch Rectangular Pitch

Fuel element pitch Hexagonal Rectangular conversion

Flow area per rod, cm2 5.464 5.532

Hydraulic diameter, mm 18.64 19.65

Rod (heated) diameter, mm 37.34 35.84

Inlet temperature, C (F) 25 (77) 30 (86)

Pressure (~mid-core), bars 1.68 1.80

Saturation temperature, C (F) 114.8 (238.6) 116.9 (242.4)

Inlet K-loss 3.58 1.672

Exit K-loss 3.0 0.6

Reactor power, MW 2.0 1.0

Number of rods 100 90

Radial power factor (hot. rod) 1.5 1.565

Power of hottest rod, kW 30.0 17.4

8

Axial Power Shape for Hottest Rod of Hexagonal Pitch TRIGA

0

0.2

0.4

0.6

0.8

1

0.2 0.4 0.6 0.8 1 1.2 1.4

Relative Power

Rel

ativ

e L

eng

th

9

Comparison of STAT and RELAP5 Results

STAT void detachment fraction is assumed to be zero.

RELAP5 fails to provide a stable (non-oscillatory) solution above 48 kW/rod.

Hexagonal Pitch TRIGA

0

20

40

60

80

100

120

140

0 10 20 30 40 50

Power Per Rod, kW

Ou

tlet

Co

ola

nt

Tem

per

atu

re,

C

STAT

RELAP5

Hexagonal Pitch TRIGA

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0 10 20 30 40 50

Power Per Rod, kW

Flo

w R

ate

Per

Ro

d,

kg/s

RELAP5

STAT

10

Representative TRIGA CHF Parameters for the Limiting Channel (Step 2)

Difficulty: Much of the published CHF measurements is focused on power reactors, which operate at high pressures and flow rates. However, TRIGA reactors operate at low pressures and at low (natural-convective) flow rates.

Nominal Conditions CHF Conditions

Mixed-mean coolant temperature

Less than boiling Less than or at boiling

Mass flux, kg/m2-s ~100 ~300

Velocity, cm/s (ft/s) ~10 (~1/3) ~30 (~1)

Pressure, bar ~1.8 ~1.8

11

CHF Correlations Considered

Bernath (1960) – Used in STAT code along with McAdams (1949) (STAT results indicate that for TRIGA reactors the Bernath correlation predicts lower CHF values than does the McAdams correlation.)

1986 Groeneveld Table – RELAP5 option

1995 Groeneveld Table – Not available in RELAP5

2006 Groeneveld Table – Not available in RELAP5

Hall and Mudawar (Purdue) – Proprietary 1998 collection of world’s CHF data in water. Has a simple correlation for subcooled boiling. for quality < −0.05 and G>300 kg/m2-s

PG-CHF (Czech Republic, ~1994) – RELAP5 rod-bundle option, 4 flavors

12

Bernath Correlation (1960)

Based on low pressure subcooled measured data

– 1956 Columbia University data• Annulus formed by 27.4-mm (1.08-inch) diameter heater inside an

unheated tube• 14 tests with approximate ranges of 2 to 4 bar, 80 to 110° C, 1800

to 9000 kg/m2-s (6 to 30 ft/s), and dh = 10.6 to 14.7 mm

– 1949 McAdams data – 0.25” heater inside 0.77” tube (dh = 13.2 mm)

Checked by Bernath against several sets of independently measured data covering a wide range of parameters

Applicable to subcooled boiling; Limited applicability to low-pressure bulk boiling

13

Bernath CHF Correlation

CHF = CHF, pound centigrade units per hr-ft2

(1 p.c.u. = 1.8 Btu)

film coefficient at CHF, p.c.u./hr-ft2-C

TWBO = wall temperature at

CHF, C

Tb = bulk coolant temperature,

C De = hydraulic diameter, ft

Di = diameter of the heated surface = heat perimeter / π, ft (In STAT code, diameter of fuel rod)

P = pressure, psia V = coolant velocity, ft/s

4

V

15P

P54Pln57T

ft0.1Dif/D1090slope

ft0.1Dif/D48slope

V(slope)DD

D10890h

TThCHF

WBO

ee

e0.6e

ie

eBO

bwBO BO

14

1986, 1995, and 2006 Groeneveld CHF Look-Up Tables

CHFtable is a function of:

– pressure (kPa)

– mass flux (kg/m2-s)

– quality – Negative values are used to represent subcooled conditions

Based on water flowing inside an 8 mm diameter tube that is heated from the periphery

Linear interpolation used for values between table entries

Multiplicative factors for other geometries and conditions

– CHFbundle = CHFtable × K1 × K2 × K3 × K4 × K5 × K6 × K7

– 1986 has 6 factors.

– Factors have changed after 1986. Later ones have 7 factors.

– Some of the newer factors are tentative or not well defined

– Most factors should be close to 1.0

15

Groeneveld K1 and K2 Factors

1986 K1 (hydraulic diameter, dh)

– For dh = 18.64 mm (hexagonal pitch TRIGA):

• 1986 => K1=0.79

• After 1986 => K1=0.66

– After 1986 / 1986 = 0.83

For K2 (rod bundle factor)

– After 1986 a tentative new relationship was suggested.

– The 1986 relationship will be assumed to apply to all years.

– It is K2 = min[ 0.8, 0.8 × exp(-0.5 × quality(1/3) ]

– Therefore, K2 = 0.8 for subcooled regions and less for bulk boiling

regions.

After 1986 K1 (hydraulic diameter, dh)

mm25dfor570.K

mm25dmm3ford

8K

h1

h

21

h1

mm16dfor0.79K

mm16dmm2ford

8K

h1

h

31

h1

16

Groeneveld K4 Factors For K4 (heated length factor)

– It appears that it has not been changed between 1986 and 2006.

– The following is based on the RELAP5 source code:• X = quality• L = heated distance from channel inlet to middle of node• D = heated diameter (i.e., 4 × flow area / heated perimeter)

• ρf and ρg are the densities of saturated liquid and vapor, respectively.

• If X < 0, X = 0• If L/D < 5, L/D = 5

• α = X / (X + ρg (1 − X) / ρf )

• K4 = exp( D/L × exp( 2 × α ) )

– For X slightly greater than 0, K4

increases rapidly with quality.This does not seem to affect thenear limiting CHF powers for thegeneric hexagonal pitch TRIGA.

Middle Node of Generic Hexagonal Pitch TRIGA

1.0

1.2

1.4

1.6

1.8

2.0

2.2

-0.2 0 0.2 0.4 0.6 0.8 1

Quality

K4

17

Errors Associated with 2006 Groeneveld Table*

For the region of the table of interest for TRIGA reactors, the CHF values are not a result of direct measurement. These regions, Groeneveld* states, “represent calculated values based on selected prediction methods …”

In addition, Groeneveld* uses smoothing methods to eliminate discontinuities that are a result of scatter in the measured data. The paper provides RMS errors between the measured data and the smoothed entries in the table. For the direct substitution method being used in the current analysis, negative qualities in the measured regions of the table have an RMS error of 14.74%. Positive quality regions have much higher RMS errors.

* D.C. Groeneveld, J.Q. Shan, A.Z. Vasić, L.K.H. Leung, A. Durmayaz, J. Yang, S.C. Cheng, and A. Tanase, “The 2006 CHF look-up table,” Nuclear Engineering and Design 237 (2007) 1909-1922.

18

Hall & Mudawar (Purdue) CHF Outlet Correlation

0

0.724

g

f

0.644

g

f

0.312

f

2

fg xρ

ρ0.9001

ρ

ρ

σρ

DGhG0.0722CHF

Symbol Variable Minimum Maximum

D Hydraulic Diameter, mm 0.25 15.0

G Mass Flux, kg/s-m2 300 30,000

Pressure, bar 1 2000

x0 Quality -1.00 -0.05

hfg Latent heat of vaporization

σ Surface tension

ρf Density of saturated liquid

ρg Density of saturated vapor

19

PG-CHF (Czech Republic) CHF Data

One of 2 CHF options built into RELAP5. (The other is Groeneveld 1986.) Based on three separate experimental databases – one for tubes, one for

rod bundles, and one for annuli. For each geometry there are four PG-CHF forms called: “Basic,” “Flux,”

“Geometry,” and “Power” (It appears RELAP5 produces obviously erroneous results for the “Basic,” “Flux,” and “Geometry” forms.)

Rod bundle database

– 153 test geometries

– 7,616 total points Data ranges for rod bundles:

– Pressure: 2.8 to 187.3 bar (TRIGA ~1.8 bar)

– Mass flux: 34.1 to 7478 kg/m2-s

– Quality: subcooled to 100% steam

– Heated length: 0.4 to 7.0 m (TRIGA 0.381 m)

– Fuel rod diameter: 5 to 19.05 mm (TRIGA ~37 mm)

20

CHF vs. Coolant Quality for 8 mm Diameter Tube1.8 bar, 300 kg/m2-s

1.8 bar, 300 kg/m2-s, 8 mm Diameter Tube

010002000300040005000600070008000

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20

Coolant Quality

Cri

tica

l H

eat

Flu

x,

kW/m

2

Purdue (outlet)

1986 Groeneveld

1995 Groeneveld

2006 Groeneveld

Bernath

Subcooled Boiling Bulk Boiling

11.5 C 38.0 C 64.4 C 90.8 C 116.9 C 116.9 C 116.9 C

Coolant Temperature

21

CHF vs. Temperature for 19.65 mm Diameter Tube1.8 bar, 300 kg/m2-s (Rectangular Pitch TRIGA)

1.8 bar, 300 kg/m2-s, 19.65 mm Diameter Tube

0

1000

2000

3000

4000

5000

6000

0.00 20.00 40.00 60.00 80.00 100.00 120.00

Coolant Temperature, C

Cri

tica

l H

eat

Flu

x,

kW/m

2

Purdue (outlet)

1986 Groeneveld

1995 Groeneveld

2006 Groeneveld

Bernath

22

CHF Ratios for Hexagonal Pitch TRIGA Evaluated at Nominal Power, where Highest Power Rod is 30kW

CHR Ratio = local CHF prediction / local heat flux Thermal-hydraulics code is shown in parentheses

Hexagonal Pitch TRIGA

1.051.061.061.071.071.081.091.101.121.141.181.221.221.221.22

0

2

4

6

8

10

12

14

16

1 2 3 4 5 6 7 8CHF Ratio

Hea

ted

Axi

al L

oca

tio

n,

Inch

es

Bernath (STAT)Bernath (RELAP)2006 Groeneveld (RELAP)1986 Groeneveld (RELAP)K4 Groeneveld Factor

Directly from RELAP5

Directly from STAT

(1 Corresponds to 30 kW/rod)

23

PG-CHF CHF Ratios for Hexagonal Pitch TRIGA Evaluated at Nominal Power, where Highest Power Rod is 30kW

RELAP5 flow except for Bernath, which uses STAT flow

PG-CHF, Basic, Geometry, Flux, & Power (RELAP)

0

2

4

6

8

10

12

14

16

1 2 3 4 5 6 7 8CHF Ratio

Hea

ted

Axi

al L

oca

tio

n,

Inch

es

Bernath (STAT)Basic

Geometry & Flux

Power

1986 Groeneveld (RELAP)

24

CHF Power Prediction of Hexagonal Pitch TRIGA Based on Groeneveld 2006 Table

Groeneveld 2006 CHF Correlation

0

10

20

30

40

50

60

70

80

90

0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

Flow of Hottest Rod, kg/s

Po

wer

of

Ho

ttes

t R

od

, kW CHF Power Based on RELAP5 Conditions

CHF Power at Equilibrium*

RELAP5 Conditions

RELAP5/Groeneveld CHF, 68.9 kW/rod, if the flow is as projected

Dashed implies linear extrapolation.

*Equilibrium is achieved by adjusting the channel power until it equals the CHF power.

62.1 kW/rod

RELAP5 quit here.

25

CHF Power Prediction of Hexagonal Pitch TRIGA Based on Bernath (1960) Correlation

Bernath (1960) CHF Correlation

0

10

20

30

40

50

60

70

80

0.06 0.08 0.1 0.12 0.14 0.16 0.18

Flow of Hottest Rod, kg/s

Po

wer

of

Ho

ttes

t R

od

, kW

RELAP5 Conditions

CHF Power at Equilibrium*

CHF Power Based on RELAP5 Conditions

RELAP5/Bernath CHF, 50.6 kW/rod

Dashed implies linear extrapolation.

*Equilibrium is achieved by adjusting the channel power until it equals the CHF power.

STAT

STAT/Bernath CHF, 37.1 kW/rod

26

CHF Power Prediction of Hexagonal Pitch TRIGA Based on Purdue (Outlet) Correlation

Not valid because at CHF conditions the mass fluxes, G, is less than 300 kg/s-m2 and the quality, X, is greater than -0.05. For a CHF power of 50.6 kW, G is 265 kg/s-m2 and X is -0.02 at the limiting axial location.

Purdue CHF Correlation (CHF Power = Channel Power)

10

20

30

40

50

60

70

0.06 0.08 0.1 0.12 0.14 0.16 0.18

Flow of Hottest Rod, kg/s

Po

wer

of

Ho

ttes

t R

od

, kW

RELAP5

RELAP5 Extrapolated

CHF Power at Equilibrium RELAP5/Purdue CHF, 50.6 kW/rod, if the flow is as projected

27

CHF Power Prediction of Hexagonal Pitch TRIGA Based on PG-CHF (~1994) Correlations

PG-CHF CHF Correlation (CHF Power = Channel Power)

0

25

50

75

100

125

150

0.05 0.1 0.15 0.2 0.25 0.3 0.35

Flow of Hottest Rod, kg/s

Po

wer

of

Ho

ttes

t R

od

, kW

RELAP5

RELAP5 Extrapolated

Basic, 124.4 kW*

Geometry, 129.7 kW* Flux & Power, 128.7 kW*

*RELAP5/PG-CHF kW/rod, if the RELAP5 flow is as projected

28

Summary of CHF Results for Hexagonal Pitch TRIGA

CHF Power = Channel Power

0

25

50

75

100

125

150

0.05 0.1 0.15 0.2 0.25 0.3 0.35

Flow of Hottest Rod, kg/s

Po

wer

of

Ho

ttes

t R

od

, kW

RELAP5 Flow

STAT Flow

Extrapolated RELAP5 Flow

Purdue CHF (50.6 kW)*

Bernath CHF (50.6 kW)*

Groeneveld 2006 CHF (68.9 kW)*

Flux & Power PG-CHF CHF (128.7 kW)*

*Power at Intersection with Extrapolated RELAP5 Flow

G=549 kg/s-m2

Xexit = 0

G=183 kg/s-m2

Maximum Calculated RELAP5 Flow, 0.1394 kg/sB – RELAP5/Bernath & B - Purdue

B – Groeneveld 2006

A

B – Flux & Power PG-CHF

A

29

Summary of CHF Results for Hexagonal Pitch TRIGA (continued)

Flow CHF CorrelationRod CHF Power, kW CHF Ratio*

A** B+ C++ A** B+ C++

STAT Bernath 37.1 52.5 1.24 1.75

RELAP5

Bernath 49.6 50.6 57.5 1.65 1.69 1.92

Purdue 48.9 50.6 1.63 1.69

Groeneveld 2006 62.1 68.9 71.9 2.07 2.30 2.40

Groeneveld 1986 100.3 3.30

PG-CHF, Basic 105.9 124.4 3.53 4.15

PG-CHF, Geometry 108.9 129.7 3.63 4.32

PG-CHF, Power or Flux 109.2 128.7 3.64 4.29

*1.0 corresponds to 30 kW for the highest power rod and 2.0 MW for the reactor.

**A (RELAP5 Flow): CHF curve at maximum calculated flow per rod (0.1394 kg/s, thin vertical

black line A-A in the previous figure), where RELAP5 flow begins to oscillate. +B (Extrapolated RELAP5 Flow): Intersection of a CHF correlation curve and a reactor flow

curve, as shown on the previous figure.++C (Not Recommended): CHF based on calculated reactor power and flow at 30 kW/rod.

30

Suggested Approach to CHF

Use the 2006 Groeneveld CHF table, with K1 (the newer one), K2, and K4, as

provided above.

Evaluate the CHF table at the power that produces CHF, i.e., CHF power = channel power.

Use RELAP5, or other suitable code, to predict flow. If flow extrapolation is needed, be conservative.

NUREG-1537, Part 1, Appendix 14.1, page 5 recommends minimum CHF ratios of at least 2.0 for reactors with engineered cooling systems. TRIGA reactors with natural-convective primary flow do not have engineered cooling systems. A minimum CHF ratio is under discussion.

31

Conclusions Flow Rate:

– For the hexagonal pitch TRIGA reactor, the RELAP5 flow rate predictions are greater than the STAT predictions, especially at power levels approaching CHF conditions.

CHF

– There is substantial uncertainty in the data. Correlation predictions differ greatly.

– The 2006 Groeneveld table, with K1, K2, and K4 as outlined above, is judged to be

the best choice for TRIGA reactors.

For the hexagonal pitch TRIGA reactor:

– The proposed 2006 Groeneveld CHF and RELAP5 flow combination (column A of the previous table) predicts 62.1 kW/rod.

– The traditional method of using the STAT code with the Bernath CHF correlation predicts 37.1 kW

– Thus, in this example, the proposed method predicts the CHF power to be 67%, i.e., (62.1/37.1 – 1) × 100%, greater.